Yes, If you have faulted on some payment of tax, then you can claim a refund for sure. Basically HMRC gives you a tax code, that your employer uses to work out how much tax to take from your pay. Which is then sent to HMRC before paying the rest to you. In most cases, you don’t have to do anything about it yourself. However, it’s worth keeping tabs on how much tax is coming out of your pay. It’s possible for your tax code to be faulty, or for you to be owed a refund on some of your work expenses.